Question: $f(t) = -7t^{2}+5t-2(g(t))$ $g(t) = 3t^{2}-5t-3$ $h(n) = 7n-2-f(n)$ $ g(f(1)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(1)$ . Then we'll know what to plug into the outer function. $f(1) = -7(1^{2})+(5)(1)-2(g(1))$ To solve for the value of $f$ , we need to solve for the value of $g(1)$ $g(1) = 3(1^{2})+(-5)(1)-3$ $g(1) = -5$ That means $f(1) = -7(1^{2})+(5)(1)+(-2)(-5)$ $f(1) = 8$ Now we know that $f(1) = 8$ . Let's solve for $g(f(1))$ , which is $g(8)$ $g(8) = 3(8^{2})+(-5)(8)-3$ $g(8) = 149$